Forget about crossing borders on a rented bike (outside Europe, that is). Not possible.
You'll need a carnet and you won't be able to get one as a non-resident in India.
Buying a bike in India and then leaving is an FAQ, please search the HUBB.
In short, you need to buy it in Nepal, where you CAN get a carnet. Seems a lot of hassle, though, just to ride the KKH.
Dunno about renting or buying in Pak. Just don't expect any big bikes...
I don't know how myuch time you want to spend, but have you considered riding to Pak & back?
Salut from Southern France, the bikers' paradise,